Many data storage media such as optical media or magnetic media have been developed to store data. With the increasing development of digitalized generation, the data storage density for the conventional data storage media is unsatisfactory. Nowadays, for dealing with such a problem, a holographic storage technology is developed by using holographic storage media to store data. A holographic storage medium has a largest capacity of about 3.9 TB (terabyte) among various storage devices. Perhaps, the holographic storage technology is succeeded after the HD-DVD or Blu-ray technology to be the most popular data storage technology.
In a typical holographic storage system, a laser beam is split into two beams by a beam splitter. These two beams are served as an object beam and a reference beam, respectively. The object beam and the reference beam are coherent. The object beam illuminates the object (pixel data or data page on data plane) and then the object scatters light onto the holographic storage medium. The object beam interferes with the reference beam to form an interference pattern such that a diffraction grating is recorded in the holographic storage medium. For reading pixel data from the holographic storage medium, the interference patterns recorded in the holographic storage medium are diffracted with the reference beam and thus a reconstructed object beam is obtained. Then, the reconstructed object beam is detected by a photo detector for obtaining the pixel data.
It is very important to remain optically stable in order for making and viewing a hologram. Any relative movement of the object beam and the reference beam may result in image shift when the pixel data are detected by the photo detector. Due to the image shift, the pixel data read from the holographic storage medium are inaccurate. For compensating the pixel data, a holographic storage system is disclosed in US Patent Publication No. 2005/0286388, which is assigned to InPhase Technologies, Inc. and the contents of which are hereby incorporated by reference. In such a holographic storage system, predetermined reserved blocks are assigned throughout each data page. By searching the reserved blocks, the image shift is realized. According to the image shift, the position errors are determined. The pixel data are then compensated according to the corresponding position errors. Therefore, it is very important to search the reserved blocks after a data page is received by the holographic storage system. After the reserved blocks are searched, the pixel data may be accurately detected and further decoded.
US Patent Publication No. 2005/0286388 also discloses a method of searching a reserved block. In accordance with InPhase's design, a reserved block having 8×8 pixel data of known pixel patterns is served as a reference block. When an image with 64×64 pixel data is read by the holographic storage system, a series of unit blocks with 8×8 pixel data are successively scanned and then correlations associated with respective unit blocks and the reference block are calculated. The unit block with the highest correlation denotes the reserved block. In a case that the real position of the reserved block in the x-axis is 3.4, the possible x-axis position of the reserved block computed by correlation is 3 because this conventional method has a resolution of one pixel. However, the resolution is not satisfied. In practice, the resolution of at most 0.05 pixel is desired in the holographic storage system.
For increasing the resolution, an interpolation method is used to determine a reserved block according to US Patent Publication No. 2005/0286388. FIGS. 1A and 1B are schematic diagrams illustrating the reserved blocks acquired by the interpolation method in an ideal situation and a real situation, respectively. In the ideal situation as shown in FIG. 1A, the initial reserved block Xbest is located at 0 in the x-axis and its nearest neighbors Xbest+1 and Xbest−1 are located at 1 and −1, respectively. Due to symmetry of the nearest neighbors Xbest+1 and Xbest−1 with respect to the initial reserved block Xbest, a proper reserved block at the position 21 is acquired by interpolating the corrections associated with the initial reserved block Xbest and its respective nearest neighbors Xbest+1 and Xbest−1. The position 21 is overlapped with the initial reserved block Xbest. In the real situation, however, an image shift is readily generated when the pixel data are read from the holographic storage medium. In the real situation, as shown in FIG. 1B, a reserved block at the position 22 is acquired by interpolating the corrections associated with the initial reserved block Xbest and its respective nearest neighbors Xbest+1 and Xbest−1. Due to the inherent property of the holographic storage system, an initial offset error 23 between the position 21 (the ideal situation) and the position 22 (the real situation) is readily generated.
FIG. 2 schematically illustrates an initial reserved block and its four nearest neighbors for computing the initial offset error. As previously described, the initial offset error is resulted from unequal similarity of pixels. As shown in FIG. 2, an initial reserved block 31 is a block with 8×8 pixel data. For computing the initial offset error, the correlations between the initial reserved block 31 and its four nearest neighbors (immediately above, below, to the left, and to the right of the initial reserved block 31 by one pixel, i.e. in the detected data page 30) are respectively computed. In other word, the initial offset error in the x-axis position is computed according to the correlation between the initial reserved block 31 and its left neighbor 32 and the correlation between the initial reserved block 31 and its right neighbor 33. Similarly, the initial offset error in the y-axis position is computed according to the correlation between the initial reserved block 31 and the neighbor immediately above the initial reserved block 31 (i.e. the block 34) and the correlation between the initial reserved block 31 and the neighbor immediately below the initial reserved block 31 (i.e. the block 35). Meanwhile, the initial offset errors resulted from unequal similarity of pixels in the x-axis and y-axis positions are realized.
As previously described, after the initial reserved block Xbest is computed by means of the correlation, a more precise x-axis position of the reserved block will be acquired by interpolating the corrections associated with the initial reserved block Xbest and its respective nearest neighbors Xbest+1 and Xbest−1. After undue experiments and simulations, however, it is found that the initial offset error is readily resulted from unequal similarity of pixels.
For solving the above drawbacks, US Patent Publication No. 2005/0286388 also discloses a method of searching a second reserved block Xbest′ by interpolating the covariance values associated with the initial reserved block Xbest and its respective neighbors Xbest+1 and Xbest−1 according to a modified centroid function β. An estimated second reserved block is determined by the following equation:
      Δ    ⁢                  ⁢          r      ⋒        =                    ∑                  i          =                      -            1                          1            ⁢                          ⁢                        (                                    Δ              ⁢                                                          ⁢                              r                                  m                  ⁢                                                                          ⁢                  ax                                                      -                          i              ⁢                                                          ⁢              β                                )                ⁢                  cov          ⁡                      (                                                            Δ                  ⁢                                                                          ⁢                                      r                                          m                      ⁢                                                                                          ⁢                      ax                                                                      -                i                            ,                              Δ                ⁢                                                                  ⁢                                  c                                      m                    ⁢                                                                                  ⁢                    ax                                                                        )                                              ∑                  i          =                      -            1                          1            ⁢              cov        ⁡                  (                                                    Δ                ⁢                                                                  ⁢                                  r                                      m                    ⁢                                                                                  ⁢                    ax                                                              -              i                        ,                          Δ              ⁢                                                          ⁢                              c                                  m                  ⁢                                                                          ⁢                  ax                                                              )                                    Δ{circumflex over (r)}: a distance between the second reserved block Xbest′ and initial reserved block Xbest, i.e. the x-axis offset        Δrmax: the x-axis position of the initial reserved block Xbest        β: modified centroid function, which is a constant        Δcmax: the y-axis position of the initial reserved block Xbest        cov(f): covariance value        
In the above equation, a more precise second reserved block Xbest′ is obtained by interpolating the covariance values associated with the initial reserved block Xbest and its respective neighbors Xbest+1 and Xbest−1 according to the modified centroid function β. In other words, the distances between the reserved block Xbest and the Xbest+1/Xbest−1 are corrected by the modified centroid function β.
Since the modified centroid function β is a constant, the x-axis initial offset error is considerable if there is large unequal similarity of pixels. Please refer to FIG. 3, which schematically illustrates some possibly offset positions resulted from the unequal similarity of pixels according to method disclosed in US Patent Publication No. 2005/0286388. For clarification, only some possibly offset positions in the range between Xbest+1 and Xbest−1 are illustrated in the drawings. As shown in FIG. 3, these offset positions are nonlinearly increased. In other words, the intervals between adjacent offset positions are not identical. As the offset position is gradually close to Xbest+1, the interval between adjacent offset positions is increased. For example, the offset position 41 has a smaller x-axis offset than the offset position 42. Under this circumstance, the second reserved block Xbest′ obtained at the offset position 41 has a larger resolution than that obtained at the offset position 42.
Although the InPhase's method is used to acquire the reserved block and compensate the position error according to the reserved block, there are still some drawbacks. For example, undue experiments demonstrated that the compensated error is still too large to comply with the stringent optical requirements of the holographic storage system.
Therefore, there is a need of providing a method for acquiring a more precise position of the reserved block to obviate the drawbacks encountered from the prior art.